The regularizer \(\phi (\mathbf {X})\)  plays a crucial role in determining the fusion quality and the complexity of the associated reconstruction algorithm. Different regularizers have been proposed over the years, many of which produce state-of-the-art results for multiband fusion. The authors in [1]} introduced a multiband extension of total variation called vector total variation (VTV), and solved the associated optimization problem using the alternating directions method of multipliers (ADMM). Sparse dictionary-based regularization was proposed in [2]}, where the dictionary and the corresponding sparse coefficients are learnt from the observed images; the associated optimization is solved using ADMM. For pansharpening, the best performing results are obtained using a variant of VTV where the gradients of the reconstructed image are matched with the observed MS image [3]}, [4]}; the optimization is performed
using fast iterative shrinkage. The authors in [5]} proposed a Bayesian regularizer where the associated optimization is performed using ADMM and block coordinate descent.
